Governors Deval Patrick of Massachusetts and Maggie Hassan of New Hampshire said in a joint statement Friday that ”all parties” in the Market Basket battle are “optimistic” a deal will be reached in which Arthur T. Demoulas buys out the company from his cousin Arthur S. Demoulas and other rival shareholders.

The governors say an agreement would also “restore (Arthur T.) to operating authority on an interim basis until the sale closes.”

A spokesperson for Arthur T. issued a statement on his behalf later Friday evening calling for the deal to be wrapped up “immediately.” The statement read:

Having submitted his final bid on Thursday and heard the statement of the Governors this evening, Arthur T. Demoulas expects that this purchase can and should be finalized immediately. The bid remains at full price and its terms are extremely favorable to the sellers. There is nothing that stands in the way of getting this done this weekend. It’s time to complete this deal so we can all get back to doing what we love doing, and that is running Market Basket.

Arthur T. has submitted what is being called a final offer for the chain. Reports suggest the company’s board is planning to meet in the next few days. On the topic of a timeline, the governors said no action will be taken with regards to protesting employees’ jobs “subject to reducing an agreement in principle to writing by Sunday.”

The governors also said they are hopeful ”employees will return to work, and stores will reopen, early next week.” Stores have not been closed during this summer’s ordeal, but you get their point.

Tom Trainor, a leader of the protest movement who was fired in July after more than 40 years with the company, said he and other protesters are “guardedly optimistic” in light of the statement. “We’re not breaking out the champagne yet,” he told Boston.com Friday evening.

The governors met with Arthur T. and his cousin, Arthur S. Demoulas, last weekend to try and help iron out a deal. Arthur T. originally made a bid to buy the company in July, a month after he was fired as CEO of the company.